closely and has certain other advantages. Second, we introduce a volatility index that provides a lower bound on the market …

In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks … traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a …-form and structural models of stochastic volatility …

in intraday jump detection is instantaneous volatility, by which intraday returns are scaled. The existing intraday jump … detection approaches assume that volatility does not change drastically over a short period, which, however, is in conflict with … empirical evidence that volatility can exhibit large movements. We tackle this problem by introducing a method with a completely …

exposure to changes in the price of the underlying stock (delta), and exposure to changes in implied volatility (vega) are …-known market, size, book-to-market, momentum, and short-term reversal factors. Additional volatility, stock, and option market …

exposure to changes in the underlying stock price (delta), and exposure to changes in implied volatility (vega) are removed …-to-market, momentum, short-term reversal, volatility, or option market factors …

volatility and other characteristics. Across stocks, trading costs are unrelated to the magnitude of momentum profits …